Problem: Simplify the following expression: $ k = \dfrac{-9y - 6}{10} + \dfrac{-5}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-9y - 6}{10} \times \dfrac{7}{7} = \dfrac{-63y - 42}{70} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-5}{7} \times \dfrac{10}{10} = \dfrac{-50}{70} $ Therefore $ k = \dfrac{-63y - 42}{70} + \dfrac{-50}{70} $ Now the expressions have the same denominator we can simply add the numerators: $k = \dfrac{-63y - 42 - 50}{70} $ $k = \dfrac{-63y - 92}{70}$